Generally, in computer science, the phrase integer is used to refer to a data type which symbolizes several finite sub-divisions of the mathematical integers. A data type is a classification for finding one of several kinds of data, such as floating-point, integer that find out the probable values for that type in particular. Variables that takes an integer value, for instance, 0, 1, 2, 3, 4, etc., are known as Integer variables. One cannot use these integer variables to store values of some other data type, such as a string of text or a Boolean variable. Boolean or logical data type is a data type, having two values (usually shown as true and false). Binary variables are a specific kind of integer variables. Binary variables can only have the value 0 or 1. They are integer variables with a maximum of 1 on them and there is always least of zero on each and every variable. In a pure integer model, all the variables are integer, otherwise, it is a mixed-integer model represented as MIP. An integer variable is a specific type of numeric variable in computer programming intended to store a mere whole number . This varies from other numeric variable types in which it is not able to store decimal numbers.
Integer variables are helpful if a programmer is in a situation to take out only the whole number from an existing numeral with a decimal value. The value can be positioned into an integer variable, in case if a decimal value is predictable but is either irrelevant or unwanted. This will obliterate the decimal portion of the value mechanically. Typically, these variables have many practical purposes. For instance, binary variables are used to identify that a particular thing may be used or not. According to the integer variables, a variable should take a multiple of a given value. For example, if one intends to have a given variable as a multiple of 25 then he can write the equation as var - 25 i = 0, where, ‘i’ is the integer variable and ‘var’ is the variable that should be a multiple of 25. Therefore, an additional variable and an additional constraint are required. The Model dimensions will amplify significantly, if there are many limited variables. However, if only a limited number of such variables are in the model, then there is no increase noticed. Instead, if the variable is substituted, then the equation becomes var = 25 i. This is the constraints and bounds, called the objective function. Consequently, variable ‘var’ is deleted from the model and substituted by 'i'. The variable ‘i’ can be considered as integer, in this case. The objective value of this substituted model will be identical as that of the initial objective value. On the other hand, to get the value of variable ‘var’, one should multiply the returned variable ‘i’ with the number 25.
Often, the variables in computer programming behave same as the variables in algebra in mathematics. A major dissimilarity between algebraic and programming variables is that computer programming languages permits the programmer to indicate the name of the variable. Conventional representation of algebra variables are usually given as “X” or “Y.” Basically, they denote an unidentified value that can be found afterward by proper manipulation. This representation could be “X,” “Y,” or any other name which provides proper specification of the variable.
Numerous computer programming languages need an integer variable and other variable types to be affirmed clearly. As a result, the programmer must indicate that the variable he is announcing is an integer. Computer programming variables store data of individual types. These data types determine how the variable can be maneuvered. An integer variable does not allow logical calculations suited to non-numeric variable types. A programming language may use a particular keyword intended for this reason. For example, the keyword for specifying an integer variable type in the C++ language is “int.” On the other hand, in some programming languages such as PERL, variables neither have to be specified nor have a type specified in advance of using the variable. In this case, the analyst finds out the variable type according to the operators used on the variable. Finding out variable types at runtime might cause issues, cosumes more system resources, and might also slow down the program. For this issue, the majority of the languages entail unambiguous variable statement.
Generally, such models are difficult to solve and solution time can increase drastically. The more integer variables there are the more time it takes to solve the model. For example, a model without the integer variables could be solved in 0.1 seconds while the same model with some of the variables integer can take quite a lot of time to manipulate.